## Assessment methodology for biological effects

### Overview

Time series of contaminant concentrations are assessed in three stages:
1. The concentration measurements each year are summarised by an annual index.
2. A regression model is fitted to the annual indices. The type of model depends on the number of years of data:
• 1-2 years: no model
• 3-4 years: mean
• 5-6 years: linear trend
• 7+ years: smoother
3. The fitted models are used to assess environmental status against available assessment criteria and evidence of temporal change in biological effect levels in the last ten years

### Calculating annual indices

Let cti, i = 1 ... nt be the biological effects measurements in year t, t = 1 ... T. The annual index in year t is the median log measurement:

y_t=text{median}{\log(c_{ti}), i=1 ...n_t}

### Modelling the annual indices

The annual indices are modelled as:

y_t=f(t)+\epsilon_t

where yt is the annual index in year t, f(t) is a smooth function of time (possibly linear) describing the underlying trend, and εt is an error term assumed to be independent and normally distributed with variance σ2.

The form of f(t) depends on the number of years of data:

1-2 years
no model is fitted as there are too few years for formal statistical analysis
3-4 years
mean model   f(t) = ¦
there are too few years for a formal trend assessment, but the mean level is summarised by ¦ and is used to assess status
5-6 years
linear trend   f(t) = ¦ + βt
the indices vary linearly with time; the fitted model is used to assess status and evidence of temporal change
7+ years
smoother   f(t) = smooth function of time
a loess smoother is fitted to the indices with a fixed window width (Fryer & Nicholson, 1999) of either 7, 9 or 11 years; the choice of window width is based on Akaike's Information Criteron (AIC); the fitted model is used to assess status and evidence of temporal change

Linear regression is described by e.g. Draper & Smith (1998). Loess smoothers were developed by Cleveland (1979). The application of loess smoothers to contaminant time series is described by Fryer & Nicholson (1999).

Cleveland WS, 1979. Robust locally-weighted regression and smoothing scatterplots. Journal of the American Statistical Association 74: 829-836.

Draper NR & Smith H, 1998. Applied regression analysis, 3rd edition. Wiley

Fryer RJ & Nicholson MD, 1999. Using smoothers for comprehensive assessments of contaminant time series in marine biota. ICES Journal of Marine Science 56: 779-790.

### Assessing environmental status and temporal trends

Environmental status and temporal trends are assessed using the model fitted to the annual indices.

Environmental status is assessed by comparing the upper one-sided 95% confidence limit on the fitted value in the most recent monitoring year to the available assessment criteria. For example, if the upper confidence limit is below the Background Assessment Concentration (BAC), then the mean index in the most recent monitoring year is significantly below the BAC and levels are said to be 'at background'.

No formal assessment of status is made when there are only 1 or 2 years of data. However, an ad-hoc assessment is made by comparing the index (1 year) or the larger of the two indices (2 years) to the assessment criteria.

Temporal trends are assessed for all time series with at least five years of data. When there are 5-6 years, there is evidence of a temporal trend if the slope β of the linear regression of yt on t is significant at the 5% level. When there are 7 or more years of data, the fitted smoother is used to test for evidence of any systematic change in levels over time; this test is also decomposed into a nonlinear and linear component. The results for each time series can be found in the statistical analysis output on the right hand side of the map under Graphics. Details of the methodology are in Fryer & Nicholson (1999). However, the summary maps focus on changes in levels in the most recent ten monitoring years (i.e. between 2003 and 2012, since the assessment only includes data up to 2012). For this, the fitted value of the smoother in 2012 is compared to the fitted value in 2003 using a t-test, with significance assessed at the 5% level. The correlation between the two fitted values is accounted for by the t-test. If the time series does not extend to 2012 then the fitted value in the last monitoring year is used instead.

Fryer RJ & Nicholson MD, 1999. Using smoothers for comprehensive assessments of contaminant time series in marine biota. ICES Journal of Marine Science 56: 779-790.